A man borrows X 5100 to be back with compound interest at the rate of 4% pa by the end of 2 yr in two equal yearly instalments. How much will each instalment be ?

Options

A. X 2704
B. X 2800
C. X 3000
D. X 2500

Answer

To solve the problem of calculating the equal yearly installments for a loan of X 5100 at a compound interest rate of 4% per annum over 2 years, we can follow these steps:

### Step 1: Understand the Problem
We need to find out how much each installment will be if a man borrows X 5100 and pays it back in two equal installments at a compound interest rate of 4% per annum.

**Hint:** Identify the principal amount, interest rate, and the number of installments.

### Step 2: Calculate the Total Amount to be Repaid
The total amount (A) to be repaid after 2 years can be calculated using the formula for compound interest:
\[ A = P(1 + r)^n \]
Where:
- \( P \) = Principal amount (X 5100)
- \( r \) = Rate of interest (4% or 0.04)
- \( n \) = Number of years (2)

Substituting the values:
\[ A = 5100(1 + 0.04)^2 \]
\[ A = 5100(1.04)^2 \]
\[ A = 5100 \times 1.0816 \]
\[ A = 5515.76 \]

**Hint:** Use the compound interest formula to find the total amount to be repaid.

### Step 3: Set Up the Equation for Equal Installments
Let the amount of each installment be \( x \). Since the installments are paid at the end of each year, the first installment will be paid at the end of the first year and the second installment at the end of the second year.

The first installment will accrue interest for 1 year, and the second installment will not accrue any interest. Thus, the equation can be set up as:
\[ x(1 + r) + x = A \]
\[ x(1 + 0.04) + x = 5515.76 \]
\[ 1.04x + x = 5515.76 \]
\[ 2.04x = 5515.76 \]

**Hint:** Set up the equation considering the interest accrued on the first installment.

### Step 4: Solve for \( x \)
Now, solve for \( x \):
\[ x = \frac{5515.76}{2.04} \]
\[ x = 2704 \]

**Hint:** Divide the total amount by the coefficient of \( x \) to find the value of each installment.

### Conclusion
Each installment that the man needs to pay back is X 2704.

**Final Answer:** Each installment is X 2704.

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